As we pre-trained the model with CGCNN encoder, the comparison with the supervised CGCNN model is the most direct and fair, and it offers insights into how self-supervised learning methods can help in predicting the crystalline material properties with a high degree of accuracy. We also compare the performance of the CT framework with other popular supervised GNN models, i.e., GATGNN[1]}, GIN[2]}, and OGCNN[3]}. All the models used for comparison are trained with the same hyperparameters as suggested in their publicly available codes. The train/validation/test split for the datasets is set to \(0.6/0.2/0.2\)  following previous standard benchmarking protocols. The test Mean Absolute Errors (MAEs) for the supervised training baselines and the CT framework are shown in Table REF . The detailed hyperparameters used for supervised models are listed in the supplementary information (Table S2).
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